RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS

作     者：Tang Liu Ningning Yan Shuhua Zhang 

作者机构：Research Center for Mathematics and Economics Tianjin University of Finance and Economics Tianjin 300222 China Institute of System Sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第1期

页      面：55-71页

核心收录：

学科分类：090801[农学-水产养殖] 0711[理学-系统科学] 07[理学] 0908[农学-水产] 08[工学] 09[农学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported in part by the National Basic Research Program (2007CB814906) the National Natural Science Foundation of China (10471103 and 10771158) Social Science Foundation of the Ministry of Education of China (06JA630047) Tianjin Natural Science Foundation (07JCYBJC14300) Tianjin University of Finance and Economics supported by the National Basic Research Program under the Grant 2005CB321701 the National Natural Science Foundation of China under the Grant 10771211 

主　　题：Optimal control problem Finite element methods Asymptotic error expansions Defect correction A posteriori error estimates. 

摘      要：Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.